Cahn-Hilliard Conserved Spinodal Growth
Find the growing wavelengths of a conserved mixture and see why its mean cannot amplify.
Free theory articleFind the growing wavelengths of a conserved mixture and see why its mean cannot amplify.
Concept & interpretation
The Cahn-Hilliard equation describes the phase separation process of a conserved mixture, where the total amount of each phase remains constant. Unlike nonconserved models, its mass conservation profoundly affects its stability and growth modes.
experiment
You can interactively explore the stability regions using the Cahn-Hilliard Conserved Spinodal Growth module.
- Set Quadratic coefficient to
-1, Mean field to0, Gradient penalty to1, and Mobility to1. - Set the Probe wavenumber to
0.5. - Observe that the growth rate is positive (0.1875), indicating the uniform state is unstable to perturbations of this wavelength, leading to phase separation.
- Change the Mean field to
0.5. Notice how the curvature becomes less negative (c = -0.25) and the maximum growth rate decreases. - Set the Probe wavenumber to
0. The growth rate is exactly 0, confirming that the mean field (k=0 mode) cannot amplify due to conservation of mass.